Construction of bivariate nonseparable compactly supported biorthogonal wavelets

2008 ◽  
Author(s):  
Jin-Song Leng ◽  
Ting-Zhu Huang ◽  
Ying-Ding Fu
Keyword(s):  
Biorthogonal Wavelets ◽  
Compactly Supported

NON-SEPARABLE 2D BIORTHOGONAL WAVELETS WITH TWO-ROW FILTERS

2005 ◽  
Vol 03 (01) ◽  
pp. 1-18 ◽  
Author(s):  
YINWEI ZHAN ◽  
HENK J. A. M. HEIJMANS
Keyword(s):  
Image Processing ◽  
Characteristic Feature ◽  
Tensor Product ◽  
Wavelet Transforms ◽  
Lifting Scheme ◽  
Efficient Implementation ◽  
Biorthogonal Wavelets ◽  
Compactly Supported

In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are prefered. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang.2 A characteristic feature of this class of wavelets is that the support of the corresponding filter comprises only two rows. We are concerned with the biorthogonal extension of this kind of wavelets. It turns out that the 2D wavelets in this class are intimately related to some underlying 1D wavelet. We explore this relation in detail, and we explain how the 2D wavelet transforms can be realized by means of a lifting scheme, thus allowing an efficient implementation. We also describe an easy way to construct wavelets with more rows and shorter columns.

Constructive Approaches to Biorthogonal Finitely Supported Ternary Wavelets and Wavelet Wraps

2011 ◽  
Vol 219-220 ◽  
pp. 504-507
Author(s):  
Jian Tang Zhao ◽  
Hong Lin Guo
Keyword(s):  
New Method ◽  
Constructive Method ◽  
Scaling Functions ◽  
Biorthogonal Wavelets ◽  
Compactly Supported ◽  
Vector Valued

In this paper, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelets is proposed. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A novel constructive method for designing a sort of biorthogonal vector-valued wavelet wraps is presented and their biorthogonality traits are characerized. Two biorthogonality formulas regarding these wavelet wraps are established.

scholarly journals Craya decomposition using compactly supported biorthogonal wavelets

2010 ◽  
Vol 28 (3) ◽  
pp. 267-284 ◽  
Author(s):  
Erwan Deriaz ◽  
Marie Farge ◽  
Kai Schneider
Keyword(s):  
Biorthogonal Wavelets ◽  
Compactly Supported

ON BIORTHOGONAL WAVELETS RELATED TO THE WALSH FUNCTIONS

2011 ◽  
Vol 09 (03) ◽  
pp. 485-499 ◽  
Author(s):  
YU. A. FARKOV ◽  
A. YU. MAKSIMOV ◽  
S. A. STROGANOV
Keyword(s):  
Numerical Experiments ◽  
Half Line ◽  
Walsh Functions ◽  
Similar Technique ◽  
Biorthogonal Wavelets ◽  
Vilenkin Groups ◽  
Compactly Supported ◽  
Positive Half

In this paper, we describe an algorithm for computing biorthogonal compactly supported dyadic wavelets related to the Walsh functions on the positive half-line ℝ+. It is noted that a similar technique can be applied in very general situations, e.g., in the case of Cantor and Vilenkin groups. Using the feedback-based approach, some numerical experiments comparing orthogonal and biorthogonal dyadic wavelets with the Haar, Daubechies, and biorthogonal 9/7 wavelets are prepared.

scholarly journals Discussion on Competition for Spatial Statistics for Large Datasets

2021 ◽  
Author(s):  
Roman Flury ◽  
Reinhard Furrer
Keyword(s):  
Spatial Statistics ◽  
Covariance Function ◽  
Likelihood Function ◽  
Large Datasets ◽  
Missing Observations ◽  
Covariance Model ◽  
Compactly Supported ◽  
Covariance Tapering ◽  
Simple Kriging ◽  
Estimated Parameters

AbstractWe discuss the experiences and results of the AppStatUZH team’s participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each of the different sub-competitions, we estimated parameters of the covariance model based on a likelihood function and predicted missing observations with simple kriging. We approximated the covariance model either with covariance tapering or a compactly supported Wendland covariance function.

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